Because of properties 2 and 3, for each g∈AgAg\in A, the operation a⁢dgasubscriptdgad_{g} defined as a⁢dg⁢(f)=[f,g]asubscriptdgffgad_{g}(f)=[f,g] is a derivation. If the set{a⁢dg|g∈A}conditional-setasubscriptdggA\{ad_{g}|g\in A\}generates the set of derivations of AAA, we say that AAA is non-degenerate.